Răspuns:
[tex]2\sqrt{3}-1[/tex]
Explicație pas cu pas:
[tex]\sqrt{13-4\sqrt{3}}=\sqrt{13-\sqrt{48}}[/tex]
[tex]\sqrt{13^{2}-48}=\sqrt{169-48}=\sqrt{121}=11[/tex]
[tex]\sqrt{13-\sqrt{48}}=\sqrt{\frac{13+11}{2}}-\sqrt{\frac{13-11}{2}}=\sqrt{12}-1=2\sqrt{3}-1[/tex]
Formula aplicata:
[tex]\sqrt{A\pm\sqrt{B}}=\sqrt{\frac{A+C}{2}}\pm\sqrt{\frac{A-C}{2}}[/tex]
[tex]C=\sqrt{A^{2}-B}\\C\in\mathbb N[/tex]
